Nontrivial classes in $H^*(Imb(S^1,\R^n))$ from nontrivalent graph cocycles

Abstract

We construct nontrivial cohomology classes of the space $Imb(S^1,\R^n)$ of imbeddings of the circle into $\R^n$, by means of Feynman diagrams. More precisely, starting from a suitable linear combination of nontrivalent diagrams, we construct, for every even number $n\geq 4$, a de Rham cohomology class on $Imb(S^1,\R^n)$. We prove nontriviality of these classes by evaluation on the dual cycles.